A Statistical Framework for Normalising GCSE Mathematics Grade Boundaries
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Description
A Statistical Method for Normalising GCSE Grade Boundaries for Fair Internal Assessment, Predicted Grade Determination and Cross-Paper Comparability.
Assessment standardisation is a central concern in educational measurement. Examination boards attempt to ensure that grades are comparable across years through statistical equating processes (Ofqual, 2018-2026). However, when institutions use past examination papers for internal assessment, those equating processes no longer apply. Consequently, institutions must adopt their own method to ensure fairness and comparability.
This study addresses the problem faced by institutions using mixed past examination papers for internal assessment in GCSE Mathematics Foundation Tier. When Paper 1 (non‑calculator) and Paper 2 (calculator) originate from different years, direct application of a single year's grade boundaries is mathematically unsound. The aim of this report is to establish a statistically grounded framework for normalising grade boundaries so that student attainment can be estimated more reliably.
Assessment comparability is a central issue in educational measurement. Examination boards attempt to maintain fairness between examination sessions through statistical moderation processes. However, once examination papers are reused as internal assessments, these national moderation mechanisms no longer apply.
When institutions select past examination papers from different years, grade boundaries become inconsistent indicators of student attainment. For example, a mark of 55 may represent a Grade 4 in one year but a Grade 3 in another. This creates a problem for internal grading systems that attempt to evaluate student progress objectively.
The purpose of this work is to develop a statistically grounded normalisation framework capable of addressing this problem. The model aggregates historical grade boundaries from multiple examination boards and calculates centralised boundaries that represent typical national standards.
For a detailed explanation of the methodology and functionality of The Grades Calculator, please visit:
https://mosaheb.co.uk/grades-calculator
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Dates
- Copyrighted
-
2026-03-03
References
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- Ofqual, 2018-2026. GCSE, AS and A level awarding. Office of Qualifications and Examinations Regulation. [Online] Available at: https://www.gov.uk/government/publications/ofqual-guide-for-schools-and-colleges-2026/ofqual-guide-for-schools-and-colleges-2026#grading [Accessed 03 03 2026].
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